So, as you've found out, TCP congestion control is a pretty complicated area.
For this particular case, because of the small requests, you're going to want to try to keep the connections open as much as possible, because one connection per request is going to take five packets each, whereas you can get the average down to a little more than two packets if you keep connections around.
NODELAY is the right thing for a game server; you want your 256 bytes delivered right away, and that's not a whole segment, so Nagle will pause unless you use NODELAY.
If your servers have loads of memory, the memory options are no big deal, new kernels have them right.
As for congestion control algorithms, you spotted Westwood. The other option is CUBIC. You can just go with one, or you can do some research and benchmark them. That could be quite a bit of work, but for 10M clients it's worth it. So, I'd be looking in to running a simulation using a traffic generator on a Mac or three (since they have the same TCP implementation as the phone), a Linux box in between acting as a router (more about this shortly) and one of your servers, to see how it goes.
Now, that middle Linux box should run ns-3 so you can simulate a more complicated path than just an ethernet switch. You then capture some packet traces on the sending end of the TCP connections, and analyse them with tcptrace or the tcptrace graphing modes of wireshark. The tcptrace documentation is a good introduction to analysing TCP congestion behaviour.
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